Question

Father's age is three times the sum of the ages of his two children. After 5years his age will be twice the sum of the ages of two children then the age of the father

Answer 1

Given :

• Father's age is three times the sum of the ages of his two children.
• After 5 years his age will be twice the sum of the ages of two children.

To Find :

• The present age of Father.

Solution :

Let the present age of Father be x years.

Let the sum of ages of two children be y years.

Case 1 :

$\sf{Father's\:age\:=\:3\:\times\:Sum\:of\:age\:of\:children}$

Equation :

$\red{\longrightarrow}$$\sf{x=3(y)}$

$\large{\boxed{\sf{x-3y=0\:...(i)}}}$

Case 2 :

Age of Father after 5 years, will be $\sf{\red{x+5\:years}}$

Age of two children after 5 years will be $\sf{\purple{y+5+5\:=\:y+10\:years}}$

Equation :

$\red{\longrightarrow}$ $\sf{(x+5)=2(y+10)}$

$\red{\longrightarrow}$ $\sf{x+5=2y+20}$

$\red{\longrightarrow}$ $\sf{x-2y=20-5}$

$\large{\boxed{\sf{x-2y=15\:\:...(ii)}}}$

Solve equation (1) and equation (2) to find the value of x and y.

Subtract equation (2) from equation (1),

$\red{\longrightarrow}$ $\sf{x-3y-(x-2y)\:=\:0-15}$

$\red{\longrightarrow}$ $\sf{x-3y-x+2y=-15}$

$\red{\longrightarrow}$ $\sf{-y=-15}$

$\red{\longrightarrow}$ $\sf{y=15}$

Substitute, y = 15 in equation (1),

$\red{\longrightarrow}$ $\sf{x-3y=0}$

$\red{\longrightarrow}$ $\sf{x=3y}$

$\red{\longrightarrow}$ $\sf{x=3(15)}$

$\red{\longrightarrow}$ $\sf{x=45}$

$\large{\boxed{\rm{\red{Present\:age\:of\:father\:=\:45\:years}}}}$

Answer 2

Given :

• Father's age is three times the sum of the ages of two children

• After 5 years his age will be twice the sum of the ages of two children

To Find :

• The age of the Father.

Solution :

Let children's age be x and y years then Father's age = 3(x+y)

After 5 years :

Children's age =

$\sf \hookrightarrow x +y + 5 + 5 \: years$

$\sf \hookrightarrow x +y + 10 \: years$

Father's age =

$\sf \hookrightarrow 3( x +y )+ 5\: years$

According to the Question :

$\longrightarrow \sf \: 3(x + y) + 5 = 2(x + y + 10)$

$\longrightarrow \sf \: 3x + 3y + 5 = 2x + 2y + 20)$

$\longrightarrow \sf \: 3x + 3y - 2x - 2y = 20 - 5$

$\longrightarrow \sf \: 3x - 2x + 3y- 2y = 20 - 5$

$\longrightarrow \sf \: x + y = 15$

Hence, Sum of age of his two children is 15 years.

We've assumed the age of Father as 3(x+y). Let's Find Father's age by putting the value of x + y = 15

$\longrightarrow \sf 3(x + y)$

$\longrightarrow \sf 3 \times 15$

$\longrightarrow \sf 45 \: years$

Hence, Age of the Father is 45 years.